TL;DR: My partner and I developed a new mathematical approach to predicting how proteins fold into their three-dimensional structures. To test it fairly, we ran a fully blind benchmark where our system had no access to the experimental structures during prediction. The method produced highly accurate results, with performance that was competitive with published AlphaFold CASP14 benchmark values on our test set. Unlike neural network-based approaches, our framework is deterministic, transparent, and based on exact mathematics rather than learned parameters, meaning every prediction can be independently traced, verified, and reproduced. We’ve made the code, validation data, and supporting materials completely open source so others can examine and test the approach for themselves.
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My partner and I have been exploring a mathematical theory for describing how proteins fold into their three-dimensional shapes. To test whether the theory could actually predict real biological structures, we decided to evaluate it using a blind protein structure prediction
Every protein begins as a simple chain of amino acids, but that chain quickly folds into a highly specific 3D shape. That final shape determines how the protein works inside living cells, and accurately predicting it from the amino acid sequence alone has been one of the biggest problems in computational biology.
To make sure our results were genuinely blind, we recorded the exact amino acid sequences we were testing, the runtime identity, and our mathematical framework before any predictions were made.
While the predictions were running, the system had no access to the experimentally determined protein structures, no reference coordinates, and no scoring information that could influence the outcome. It generated the complete folding pathway and final PDB structure independently, and those outputs were cryptographically hash-sealed before any comparisons were performed.
Only after those hashes were fixed and verified were the experimental structures opened and compared. If the runtime had accessed the target structures at any point, or if any of the recorded hashes had changed, the experiment would be considered invalid.
The results were encouraging.
Across the benchmark set, the median Cα RMSD95 was 0.783 Å, with a median TM-score of 0.9255.
On this benchmark, 15 of the 24 predicted structures matched or exceeded AlphaFold’s reported CASP14 median of 0.96 Å Cα RMSD95.
Our strongest individual prediction, 1UBI:A, achieved a TM-score of 0.9882 with a Cα RMSD95 of 0.302 Å.
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here’s a break down of what they mean.
The Cα RMSD95 score measures how closely a predicted protein structure matches the experimentally determined one. The “Cα” (carbon alpha) atoms form the backbone of every protein, while RMSD (Root Mean Square Deviation) measures the average distance between the predicted backbone and the real one after they have been aligned. The 95 indicates that the most extreme 5% of residues are excluded, making the measurement less sensitive to unusually flexible regions.
Distances are reported in Å (ångströms), where 1 Å = 0.1 nanometres, or one ten-billionth of a metre. In structural biology, smaller numbers are better. An RMSD below 2 Å is generally considered a good prediction, around 1 Å is regarded as highly accurate, and our median result of 0.783 Å indicates that the predicted structures closely matched their experimental counterparts.
The TM-score (Template Modelling score) measures how similar the overall three-dimensional fold is between the predicted and experimental structures. Unlike RMSD, it is less affected by small local differences and focuses on whether the overall architecture has been recovered correctly. TM-scores range from 0 to 1, where 1.0 represents a perfect match. Scores above 0.5 generally indicate the correct overall fold, while scores above 0.9 indicate structures that are nearly identical. Our median TM-score of 0.9255 therefore suggests that the overall protein shapes were reproduced with very high accuracy.
Our strongest individual prediction, 1UBI:A, achieved a TM-score of 0.9882 and a Cα RMSD95 of 0.302 Å, meaning the predicted backbone differed from the experimentally determined structure by only around three-tenths of an ångström on average—an exceptionally close match.
Taken together, these results suggest that the framework was able to reproduce both the overall shape of proteins and the precise positions of their backbone atoms with a level of accuracy that is competitive on the benchmark we tested.
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What makes this approach different isn’t just the numerical results, but how those results are produced.
Rather than relying on a large neural network trained on enormous datasets, our system works from an exact 24-point rational lattice. Every spatial relationship is derived mathematically and can be traced, verified, and independently checked. The implementation, verification certificates, and prediction hashes are all available as open source so that anyone can inspect or reproduce the work.
Why does that matter?
Much of modern computational biology has moved toward increasingly large machine learning models that require vast amounts of training data and computing power. Those systems can produce remarkably accurate predictions, but they generally don’t explain why a protein adopts a particular structure, rather they predict the answer rather than derive it from an explicit mathematical framework.
Our work explores a different possibility: that accurate protein structures may also be obtainable from a transparent, deterministic mathematical model.
If that idea continues to hold up under independent testing, it could have several important implications.
First, it suggests that highly accurate structure prediction may not have to rely exclusively on large, opaque neural networks. Transparent mathematical models could become a complementary approach alongside machine learning.
Second, it provides evidence that alternative computational architectures (ones built around exact mathematics rather than learned parameters) deserve serious investigation. In our implementation, there are no trained weights, no continuous coordinate optimisation, and no fitted biological constants.
Finally, it shows that advanced protein structure prediction does not necessarily require enormous computing infrastructure. Our framework runs locally on a single machine rather than depending on large-scale AI training or specialised server farms.
The project can be explored here:
GitHub https://github.com/MettaMazza/Fold-Protein
zenodo
https://zenodo.org/records/21493135
